Fill This Form To Receive Instant Help
Fill This Form To Receive Instant Help
Homework answers / question archive / Double Marginalization Q The 2 Suppose that the market demand for a product is given by P = 240 marginal cost of manufacturing the product is $30, the marginal cost of selling the good is $10
Double Marginalization Q The 2 Suppose that the market demand for a product is given by P = 240 marginal cost of manufacturing the product is $30, the marginal cost of selling the good is $10. A. If there is a single firm that produces the product and sells the product, what price will be set, what profits will it earn? B. Suppose that there are instead two firms, a manufacturer and a retailer. The Manufacturer set a price Prs that it sells the good to the retailer. The retailer then sets a price to sell to consumers. Set-up the maximization problem for the retailer. Solve this problem and write the solution as Pn(Q). Now using Pm(Q), set-up and solve the manufacturing firms maximization problem. What price does it set? What are the profits for each firm. 11.
A) When a single product is manufacturing and selling product the the total marginal cost will be equal to $40.
Now,
P=240-Q/2
R=P*Q
R=240Q-Q2/2
MR=dR/dQ
MR=240-Q
At profit maximizing quantity MC=MR
240-Q=40
Q=200 and
P=240-200/2
P=$140
Profit=TR-TC
Profit=200*140-200*40=$20,000.
B.i)
Let the price for manufacturer be Pm and the price for retailer be P.
The marginal profit for retailer will be P-Pm-10 and quantity sold will be Q=480-2P
The profit for retailer would be (P-Pm-10)(480-2P)
PR=480P-480Pm-4,800-2P2+2PmP+20P
For profit maximization the derivative of PR with respect to P will be zero
0=500-4P+2Pm
Pm=2P-250
or
P=Pm/2+125
ii)
The marginal profit for manufacturer will be Pm-30
The profit for retailer would be (Pm-30)(240-Pm)
PR=240Pm-7,200-Pm2+30Pm
For profit maximization the derivative of PR with respect to P will be zero
0=270-2Pm
Pm=$135
or
P=135/2+125=$192.5
The profit for manufacturing firm is
Profit=(Pm-$30)*Q=($135-$30)*200=$21,000
The profit for retailer is
Profit=(P-Pm-$10)*Q=($192.5-$135-$10)*200=$9,500
